Audio amplitude unwrapping

Abstract

A computer-implemented method for restoring a wrapped audio signal comprising a plurality of digitised signal samples at respective sample times, the method comprising: estimating a sequence of corrections comprising a sequence of numerical values the estimating comprising, for each signal sample: applying, at the sample time, a numerical filter to each of a set of potential corrections to determine a filtered value associated with each set of potential integer corrections wherein the filter enhances the filtered value at sample times when a change in a degree of wrapping occurs relative to sample times when a change in degree of wrapping does not occur; determining a cumulative objective over a plurality of signal samples by accumulating objective values and determining a sequence by selecting for each sample time a correction from the set of potential corrections wherein the correction for each sample time are selected to optimise the cumulative objective.

The invention claimed is: 
     
       1. A computer-implemented method for restoring a wrapped audio signal, wherein the wrapped audio signal comprises a plurality of digitised signal samples at respective sample times, the method comprising:
 estimating a sequence of corrections comprising a sequence of numerical values to be applied to corresponding values of the plurality of digitised signal samples of the wrapped audio signal, or estimating a sequence of corrected signal samples, the estimating comprising, for each digitised signal sample: 
 applying, at the sample time, a numerical filter to each of a set of potential corrections or set of potential corrected signal samples to determine a filtered value associated with each set of potential corrections or set of potential corrected signal samples, 
 wherein the corrections are integers or the potential corrected signal samples comprise signal samples modified by integer multiples of a correction constant, 
 wherein the numerical filter enhances the filtered value at sample times when a change in a degree of wrapping occurs relative to sample times when a change in degree of wrapping does not occur; 
 determining a cumulative objective over a plurality of signal samples by accumulating objective values, each objective value being determined by applying an objective function to the filtered value associated with each set of potential corrections or set of potential corrected signal samples; and 
 determining a sequence of corrections or sequence of corrected signal samples, one for each digitised signal sample, by selecting for each sample time a correction or corrected signal sample from the set of potential corrections or set of potential corrected signal samples for the sample time, wherein the correction or corrected signal sample for each sample time are selected to optimise the cumulative objective; and 
 determining a restored version of the wrapped audio signal using the sequence of corrections or corrected signal samples. 
 
     
     
       2. A method as claimed in  claim 1  wherein a potential wrapping state comprises a potential correction from the set of potential corrections or a potential corrected signal sample from the set of potential corrected signal samples, and wherein there are multiple potential wrapping states for each sample time; the method further comprising:
 determining the cumulative objective, for each of a set of paths, each path comprising a time sequence of the potential wrapping states, one for each sample time, 
 wherein the cumulative objective is determined for a path by accumulating the objective value from the filtered value for transitioning from each potential wrapping state in the path to the next potential wrapping state in the path, and 
 wherein the filtered value for transitioning from each potential wrapping state in the path to the next potential wrapping state in the path is determined for the plurality of potential corrections or plurality of potential corrected signal samples defined by both the potential wrapping state and next potential wrapping state; and 
 identifying an optimum path which identifies the sequence of corrections or corrected signal samples used to determine the restored version of the wrapped audio signal. 
 
     
     
       3. A method as claimed in  claim 1  wherein a potential wrapping state comprises a plurality of potential corrections from the set of potential corrections or a plurality of potential corrected signal samples from the set of potential corrected signal samples, and wherein there are multiple potential wrapping states for each sample time; the method further comprising:
 determining the cumulative objective, for each of a set of paths, each path comprising a time sequence of the potential wrapping states, one for each sample time, 
 wherein the cumulative objective is determined for a path by accumulating the objective value from the filtered value for transitioning from each potential wrapping state in the path to the next potential wrapping state in the path, and 
 wherein the filtered value for transitioning from each potential wrapping state in the path to the next potential wrapping state in the path is determined for the plurality of potential corrections or plurality of potential corrected signal samples defined by both the potential wrapping state and next potential wrapping state; and 
 identifying an optimum path which identifies the sequence of corrections or corrected signal samples used to determine the restored version of the wrapped audio signal. 
 
     
     
       4. A method as claimed in  claim 1  wherein the objective function is a cost function and the cumulative objective is a cumulative cost, and wherein the correction or corrected signal sample for each sample time are selected to minimise the cumulative cost determined from the cost function. 
     
     
       5. A method as claimed in  claim 1  wherein the objective function is a probability function and the cumulative objective is a cumulative likelihood, and wherein the correction or corrected signal sample for each sample time are selected to maximise the cumulative likelihood determined from the probability function. 
     
     
       6. A method as claimed in  claim 1 , wherein the corrections are chosen from a discrete set of integers between an upper and lower bound. 
     
     
       7. A method as claimed in  claim 1 , wherein the wrapped audio signal possesses at least one region of the plurality of digitised signal samples at respective sample times having wrapped amplitude, and
 wherein the restored audio signal possesses an amplitude at each sample time determined to be a most-likely original amplitude of a source audio signal. 
 
     
     
       8. A method as claimed in  claim 1 , the method further comprising:
 refining a previous estimation of the restored audio signal, the refining comprising: 
 reusing the previous estimation of the restored audio signal as a further input audio signal; 
 estimating one or more further sequence of corrections comprising a sequence of numerical values to be applied to corresponding values of the plurality of digitised signal samples of the further input audio signal, or estimating a further sequence of corrected signal samples; 
 determining a refined restored version of the wrapped audio signal using the further sequence of corrections or further corrected signal samples. 
 
     
     
       9. A method as claimed in  claim 8 , wherein a further numerical filter is applied for each reuse of the previous estimation of the restored audio signal as a further input audio signal. 
     
     
       10. A method as claimed in  claim 1 , wherein the numerical filter is a predetermined numerical filter comprising one or more constant numerical values. 
     
     
       11. A method as claimed in  claim 1  wherein the numerical filter is predetermined, and wherein the numerical filter is determined from a representative clean audio signal having unwrapped audio. 
     
     
       12. A method as claimed in  claim 1 , wherein the numerical filter is a time dependent numerical filter, and
 wherein the time dependent numerical filter is varied for at least one of the signal-samples for which the numerical filter is applied. 
 
     
     
       13. A method as claimed in  claim 12 , wherein the calculation of the time dependent numerical filter is based on one more properties of one or more local regions of the wrapped audio signal, and wherein each local region comprises a plurality of digitised signal samples. 
     
     
       14. A method as claimed in  claim 1 , the method comprising:
 processing the wrapped audio signal before estimating the sequence of corrections or estimating the sequence of corrected signal samples, the processing comprising: 
 applying to each of the plurality of digitised signal samples a distortion-likelihood function to provide a plurality of distortion-likelihood values; 
 determining a subset of signal samples from the plurality of digitised signal samples, wherein the determining is based on comparing the plurality of distortion likelihood-values to a threshold value. 
 
     
     
       15. A method as claimed in  claim 14 , wherein the subset of signal samples comprises signal samples at sample times when a change in the degree of wrapping is determined to be likely relative to nearby signal-samples. 
     
     
       16. A method as claimed in  claim 14 , further comprising:
 determining the cumulative objective, for each of a set of paths, each path comprising a time sequence of the potential wrapping states, one for each sample time, 
 wherein the cumulative objective is determined for a path by accumulating the objective value from the filtered value for transitioning from each potential wrapping state in the path to the next potential wrapping state in the path, and 
 wherein the filtered value for transitioning from each potential wrapping state in the path to the next potential wrapping state in the path is determined based only on the subset of signal samples. 
 
     
     
       17. A non-transitory computer-readable medium having executable processor control code to, when executed, implement the method of  claim 1 . 
     
     
       18. A signal processing system for restoring a wrapped audio signal, wherein the wrapped audio signal comprises a plurality of digitised signal samples at respective sample times, the system comprising one or more processors configured to:
 estimate a sequence of corrections comprising a sequence of numerical values to be applied to corresponding values of the plurality of digitised signal samples of the wrapped audio signal, or estimate a sequence of corrected signal samples, the estimating comprising, for each digitised signal sample: 
 applying, at the sample time, a numerical filter to each of a set of potential corrections or set of potential corrected signal samples to determine a filtered value associated with each set of potential corrections or set of potential corrected signal samples, 
 wherein the corrections are integers or the potential corrected signal samples comprise signal samples modified by integer multiples of a correction constant, 
 wherein the numerical filter enhances the filtered value at sample times when a change in a degree of wrapping occurs relative to sample times when a change in degree of wrapping does not occur; 
 determining a cumulative objective over a plurality of signal samples by accumulating objective values, each objective value being determined by applying an objective function to the filtered value associated with each set of potential corrections or set of potential corrected signal samples; and 
 determine a sequence of corrections or sequence of corrected signal samples, one for each signal sample, by selecting for each sample time a correction or corrected signal sample from the set of potential corrections or set of potential corrected signal samples for the sample time, wherein the correction or corrected signal sample for each sample time are selected to optimise the cumulative objective; and 
 determine a restored version of the wrapped audio signal using the sequence of corrections or corrected signal samples.